In many environments, backups are performed using multiple streams. Each stream represents a physical/virtual connection between the source system (storing the data sets) and the target system (storing a copy of the data sets after the backup is completed). One reason for having multiple streams is to reduce the backup window (the duration taken to perform the backup of a sequence of data sets) by performing the backups of multiple data sets concurrently. Even in such environments, it may still be desirable to further reduce the backup window.